Download Comparing and Ordering Integers

Chapter 2
Integers
+-*÷
Integers
Integers- Negative and Positive whole
numbers. INCLUDES 0
Write some integers on your paper:
…-4, -3, -2, -1, 0, 1, 2, 3, 4…
Ordering integers
Order the following from least to greatest:
1) -7, 2, -1, 0, -2
-7, -2, -1, 0, 2
2) 9, -4, 12, -11, -1
-11, -4, -1, 9, 12
3) 0, -99, 44, -60, 16
-99, -60, 0, 16, 44
Absolute Value
Absolute Value- The distance between the
number and zero on a number line.
The absolute value of n looks like: │n│
Find the absolute value of the following:
│6│
│-8│
│15│
Opposite
Opposite of a number- same distance from
0. On different sides of 0. Opposite
numbers have the same AV.
Find the opposite:
-6
14
-27
Evaluate:
-│8│
-│-5│
(-6)
-(- 4)
Do Now 9/30
Write the opposite and Absolute Value:
1) 18
2) -45
3) -16
Evaluate:
4) -(-2)
5) - │-18│
Adding Integers – Number Line
Use your number line to add integers:
Positive numbers right, Negative numbers left
1)
3 + (-4)
1)
2)
3)
2)
-5 + 2
Start at zero
Move 3 units to the right
Move 4 units to the left
1) Start at zero
2) Move 5 units to the left
3) Move 2 units to the right
Adding Integers – Number Line
Use your number line to add integers:
Positive numbers right, Negative numbers left
3) -6 + -1
4) -4 + 2
1) Start at zero
2) Move 6 units to the left
3) Move 1 unit to the left
1) Start at zero
2) Move 4 units left
3) Move 2 units right
Do Now 10/1/09
Add using a number line:
1) 7 + (-10)
2)
-2 + ( -3)
3)
-8 + 5
4)
5+3
Adding Integers- Walking on a
number line
1)
2)
3)
4)
5)
6)
7)
8)
-2 + 4
7 + (-8)
-6 + -3
5 + (-4)
-8 + 3
-2 + (-7)
12 + (-8)
-16 + 9
9) 9 + (-11)
10) -6 + 14
11) 17 + (-7)
12) -14 + - 6
13) 7 + (-4)
14) -8 + 8
15) -12 + (-7)
16) 15 + (-8)
17) 19 + (-11)
18) -16 + 3
19) 7 + (-7)
20) -16 + - 2
21) 15 + (-8)
22) -8 + 3
23) -12 + (-2)
24) 19 + (-7)
What are the Adding Integer
RULES?!
Write a rule for:
(+) + (+)
(-) + (- )
( - ) + (+) / (+) + (- )
Adding Integers - Integer song:
Integer Operations Song
(Row Row Row Your Boat)
 Same sign - add and keep
 Different sign - subtract
 Keep the sign of the bigger number
 Then you’ll be exact.
Adding Integers – Using the Song
1) -3 + -4
3) -20 + -30 5) -6 +1 +-3
2) -8 + -5
4) 7 + -8
7) 33 + -15
9) -47 + -20 11) 7 + -13 + 6
8) -29 + -64
10) -8 + 75 12) -19 + 48 + -5
6) 4 + -7 + -11
Do Now 10/5
Add:
1) -35 + 42
2)
-64 + -37
3) 73 + -19
4) -128 + -84
Adding Integers – Zero Pairs
zero pairs- is a pair of numbers whose
sum is zero.
1)
2)
3)
4)
4 + -7
3 + -2
-6 + 5
-3 + - 4
Subtracting Integers – Add Opposite
Subtract Integers- Add the opposite of the
second number.
1)
11 – 12
2)
-5 – 3
3)
-7 – (-6)
4)
8 – (-2)
Do Now 10/7/09
Subtract – Add the opposites
1) -6 – 9
2)
72 – 114
3)
-18 – (-88)
4)
25 – (-93)
Subtracting Integers –Song
Subtract – no, don’t do!
 Just change the second sign
 Now add the numbers like you did
 And then you will be fine

Subtracting Integers – Using the
song
1) -3 – (-4)
3) 20 – (-30) 5) -6 - 1 - 3
2) -8 – (-5)
4) 7 – (-8)
6) 4 - (-7) – (-11)
7) 33 – (-15) 9) -47 – (-20) 11) 7 – (-13) - 6
8) -29 - 64
10) -8 - 75
12) -19 - 48 – (-5)
Do Now- 10/8/09
Subtract:
1) -8 – (-3)
2)
- 74 – 19
3)
-56 – (-32)
4)
43 – 93
Adding and Subtracting Integers
Be careful, you have to decide which rule
to follow (adding or subtracting)
6) - 5 – 28
1) -54 + 84
7) 19 – 57
2) - 35 – 32
8) 38 + -45
3) 49 – 9
9) -79 + -11
4) 23 + -84
10) -42 – 34
5) -34 - 63
Do Now 10/14/09
Add or subtract:
1) 14 + -12
2)
48 – 59
3)
-71 + - 34
4)
-84 - 49
Multiplying and Dividing IntegersMultiply and Divide numbers
as you normally do.
-If both signs are positive or negative the
answer is positive
-If one sign is positive and one sign is
negative the answer is negative
Multiply and Divide
1)
-12 ÷ 3
5) 49 ÷ -7
2)
-14 * -7
6) -30 ÷ -10
3)
-35 ÷ -5
7) -7 * 3
4)
6 * -5
8) -9 * -2
Do Now 10/15
1) 20 * (-3)
2) 16 ÷ (-8)
3) -40 ÷ (-20)
4) -8 * 5
Multiplying and Dividing with Zeros
Zero – 0
Multiplying0 * -32 = 0
Dividing0 ÷ -4 =
0
-4
=
0
-4 ÷ 0= -4
0
=
undefined = u
Multiplying and Dividing IntegersSong
Multiply or Divide - what do I do now?
 Same sign- positive –
Different sign- negative
 I got it now KERPOW!!

Multiplying and Dividing IntegersSong
1)
-10 ÷ 5
5) 49 ÷ -7
2)
-2 * -7 * 5
6) -110÷ -10
3)
-90 ÷ -5
7) -7 * -4 * -2
4)
6 * -3 * -3
8) -9 * -12
Do Now 10/16
Add/subtract/Multiply and Divide
1. 5 + -3
2.
-3 * 7
3.
-28 ÷ -2
4.
14 – (-8)
Peer Grading of projects
1.
2.
3.
Tell what Grade you should get and
why on back of rubric.
Show each other all the rules on your
project. (check that each person
included all parts of the rules)
Show each other all the real life
examples on your project. (check that
there are atleast 3 and that they are
different ideas).
Do Now: Identify the following properties of
Math (use your text if you forgot):
1- Identity PropertySum of a number and zero = the number
Product of a number and 1 = the number
a+0=a
b*1=b
2- Commutative PropertyCan add or multiply numbers in any order
a+b = b +a
cd= dc
3-Associative PropertyChanging the grouping will not affect the sum or product
a + (b+c) = (a + b) + c
abc= cba
Distributive PropertyYou can multiply a number and a sum by
multiplying the number by each part of the sum
and then adding these products. The same
applies to subtraction.
A(B + C) = AB + AC
D(E – F) = DE – DF
Ex1: -5 (x + 10)
-5x + -5(10)
= -5x + -50
or
= -5x – 50
 Ex2:
2 (x - 7)
2x - 2(7)
= 2x - 14
Ex3: 3 [x – 20 + (-5)]
3 (x) – 3 (20) + 3 (-5)
3x – 60 + (-15)
3x + (-60) + (-15)
3x + (-75)
Simplify using Distributive Property
1) -2 (5 + 12)
2) -4(-7 – 10)
3) 2(w – 8)
4) -8(z + 25)
Tell Which property each displays:
Do Now 10/28
1) 3(2x + 1)= 6x +3
2) (2 + 4) + y = 2 + (4 + y)
3)
4x = x*4
4)
6(2*15)= (6*2)15
Like Terms- Identical variable parts
raised to the same power
For example: 2m and 14m
3x4 and 12x4
12xy2z and xy2z
3 and 62
Write 3 more examples on your page:
Simplify the expression by combining
like terms:
1.
c + 8c
2.
3m + -4m
3.
15y2 + 9y + 11y2
4.
-5x -7t +2x -9t
Like Terms1.
5x – 2x
2.
2a + 3a
3.
7p – 3p + 25
4.
10k + 21+ -8k
5.
13z + 7 - 5z
Simplify the expressions:
1.
9w (w + -4)
2.
8(1 +4d) – 3d
3.
9p – ( 7p + 2)
4.
11(2g - 4) +12 -18g
Solve Equations Involving
Distribution

3(x – 9) = -39

z + 4(6 – z) = 21

8 = -7(y + 1) + 2y